A Unified Einstein-Yukawa Theory

Following Schrodinger's hint that the charge independence of nuclear forces is analogous to the mass-independence of the gravitational interaction required by the equivalence principle, we construct a non-Riemannian geometry in which the worldlines of particles moving in combined gravitational and scalar meson fields are the paths of space-time. A geometric Lagrangian which yields the coupled Einstein-Yukawa equations is given. A characteristic "order of magnitude" difficulty of geometric unified field theories can be examined here in closed form.